Yes you can install Windows XP onto a FAT16 partition. Setup gives you the option to.
If the partition is too large, you will be able to format only using the NTFS file system. If it is below 2048 megabytes, you can format it as FAT16. If it is over 2047 megabytes, you can format the partition as FAT32.
If you want to install XP to a floppy, you can't.